15n(n+1)=4n-2

Solution for 15n(n+1)=4n-2 equation:

15n(n+1)=4n-2

We move all terms to the left:

15n(n+1)-(4n-2)=0

We multiply parentheses

15n^2+15n-(4n-2)=0

We get rid of parentheses

15n^2+15n-4n+2=0

We add all the numbers together, and all the variables

15n^2+11n+2=0

a = 15; b = 11; c = +2;
Δ = b2-4ac
Δ = 112-4·15·2
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-1}{2*15}=\frac{-12}{30}
=-2/5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+1}{2*15}=\frac{-10}{30}
=-1/3
$